Lemma 5.6 ([1]} Lemma 7.8) 
Let \(W \rightarrow X\)  be a morphism of log schemes, which is transverse to \(\mathfrak {M}^{ev}(\mathcal {X},\beta ) \rightarrow X\) . Letting \(ev_{x_{out}}: \mathfrak {M}^{ev}(\mathcal {X},\beta ) \rightarrow X\)  be the morphism of log stacks which evaluates a log curve at the contact order 0 marked point \(x_{out}\) , then the projection \(\mathfrak {M}^{ev}(\mathcal {X},\beta )_W := W \times ^{fs}_X \mathfrak {M}^{ev}(\mathcal {X},\beta ) \rightarrow W \)  is flat with equal log and standard fiber dimension.

